具有可解释性的通用神经关闭模型
Abhinav Gupta1, Pierre F J Lermusiaux2
1Department of Mechanical Engineering, Center for Computational Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.
Scientific reports
|June 30, 2023
概括
本研究引入了统一的神经局部延迟微分方程,以改进计算物理中的机器学习模型. 新的框架提高了动态系统的解释性,概括性和计算效率.
科学领域:
- 计算物理 计算物理
- 机器学习 机器学习
- 科学计算科学计算
背景情况:
- 计算物理学中的动态模型往往缺乏预测能力,并且在计算上昂贵.
- 现有的机器学习方法在各种条件下难以解释和概括.
研究的目的:
- 开发一种通用的方法,以解决机器学习增强动态模型的可解释性,概括性和计算成本挑战.
- 为增强预测建模引入统一的神经局部延迟微分方程.
主要方法:
- 增强现有的部分微分方程 (PDE) 模型,使用马科维亚和非马科维亚神经网络 (NN) 闭包参数化.
- 开发一个灵活的框架来设计使用各种 NN 架构和输入库的未知闭包条款.
- 在各种计算物理代码和机器学习框架中获得辅助的PDEs,以便直接实现.
主要成果:
- 一般化神经关闭模型 (gnCMs) 框架在不同的分辨率,条件和参数中展示了改进的概括性.
- 学习的gnCMs成功发现了缺失的物理,确定了数值错误术语,并提供了可解释的见解.
- 该框架显示了计算优势,并弥补了简单模型中的局限性.
结论:
- 统一的神经局部延迟微分方程提供了一种强大的方法来增强计算物理中的动态模型.
- 开发的gnCMs框架在解释性,概括性和计算效率方面取得了显著的改进.
- 这种方法为更强大,更通用的基于物理的机器学习应用程序铺平了道路.
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